In order to send files to the other Mac on the same local network, usually we will utilize a public folder and create a drop box inside. Drop Box is a folder where other users can drop files into it, but they can't see the content inside.
The drop box creation is simple and straightforward:
However, you also need to turn on your File Sharing so that other users on the local network can access to your Public Folder.
You can go inside System Preferences → Sharing to turn on your File Sharing. Now, you should be able to share files easily on the local network.